Yingfang Zhou

Dynamic Capillary Pressure Curves from Pore-Scale Modelling in Mixed-Wet Rock Images

In several reservoir multiphase flow processes, such as fracture and near well-bore flow, both viscous and capillary forces determine the pore-scale fluid configurations due to high flow rates. This gives rise to significant dynamic effects in the capillary pressure relation because the fluids are redistributed faster than the relaxation time required for transitions between capillary-equilibrium states. We simulate quasi-static and dynamic capillary pressure curves for drainage and imbibition directly in SEM images of Bentheim sandstone at mixed-wet conditions by treating the identified pore spaces as tube cross-sections. Stepwise pressure differences are imposed between inlet and outlet. The phase pressures vary with length positions but remain unique in each cross-section, which leads to a nonlinear system of equations that are solved for interface positions as a function of time. The cross-sectional fluid configurations are computed accurately at any capillary pressure and wetting condition by combining free energy minimisation with a menisci-determining procedure that identifies the intersections of two circles moving in opposite directions along the pore boundary. Circle rotation at pinned contact lines accounts for mixed-wet conditions. Dynamic capillary pressure is calculated using volume-averaged phase pressures, and dynamic capillary coefficients are obtained from the rates of saturation change. The results could be applied in reservoir simulation models to assess dynamic pore-scale effects on the Darcy scale. Consistent with measurements, our results demonstrates that dynamic capillary pressure is higher than the static capillary pressure during drainage, but lower during imbibition. The dynamic capillary coefficients and rates of saturation change during imbibition depend strongly on wettability and initial water saturation. The proposed model provides insights into the extent of dynamic effects in capillary pressure curves for realistic mixed-wet pore spaces, which contributes to improved interpretation of core-scale experiments.

Simulation of Three‑Phase Capillary Pressure Curves Directly in 2D Rock Images

Pore-scale modeling of three-phase capillary pressure in realistic pore geometries could contribute to an increased knowledge of three-phase displacement mechanisms and also provide support to time-consuming and challenging core-scale laboratory measurements. In this work we have developed a semi-analytical model for computing three-phase capillary pressure curves and the corresponding three-phase fluid configurations in uniformly-wet rock images encountered during tertiary gas invasion. The fluid configurations and favorable entry pressure are determined based on free energy minimization by combining all physically allowed gas-oil, gas-water, and oil-water arc menisci in various ways. The model is shown to reproduce all threephase displacements and capillary entry pressures that previously have been derived in idealized angular tubes for gas invasion at uniform water-wet conditions. These single-pore displacement mechanisms include (i) gas invasion into pores occupied by oil and water leading to simultaneous displacement of the three fluids, (ii) simultaneous invasion of bulk gas and surrounding oil into water filled pores, and finally (iii) the pure two-phase fluid displacements in which gas invades pores occupied by either water or oil. The proposed novel semi-analytical model is validated against existing analytical solutions developed in a star-shape pore space, and subsequently employed on an SEM image of Bentheim sandstone to simulate three-phase fluid configurations and capillary pressure curves at uniform water-wet conditions and different spreading coefficents. The simulated fluid configurations for the different spreading coefficients show similar oil layer behaviour as previously published experimental three-phase fluid configurations obtained by computed microtomography in Bentheim sandstone. The computed saturation paths indicate that three-phase oil-water capillary pressure is a function of the water saturation only, whereas the three-phase gas-oil capillary pressure appears to be a function of two saturations. This is explained by the three-phase displacements occurring in the majority of the simulations, in which gas-water interfaces form immediately during gas invasion into oil- and water-saturated pore shapes.